Cholesky decomposition

:
Let sij be the (i; j) entry of S, we use the following algorithm to calculate S:
s11 = pa; s21 = b=s11; s22 =
q
c 􀀀 s2
21:
Show that this algorithm is backward stable. Namely, the computer result (using
oating
point operations) S~ satises S~S~T = A~ for some A~ close to A.